| Directions: (1 - 11) The following questions consist of two statements, one labelled as "Assertion [A] and the other labelled as Reason [R]". You are to examine these two statements carefully and decide if Assertion [A] and Reason [R] are individually true and if so, whether the Reason [R] is the correct explanation for the given Assertion [A]. Select your answer from following options. |
| Assertion [A]: The function \[x+\frac{5}{x},\,\,x\ne 0\] is strictly decreasing |
| Reason [R]: For strictly decreasing function\[~f'\left( x \right)<0.\] |
A) Both A and R are individually true and R is the correct explanation of A.
B) Both A and R are individually true and R is not the correct explanation of A.
C) 'A' is true but 'R' is false
D) 'A' is false but 'R' is true
E) Both A and R are false.
Correct Answer: A
Solution :
Given \[f(x)=3+\frac{5}{x}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,f'(x)=0-\frac{5}{{{x}^{2}}},\,\,\,x\ne 0\] Since \[{{x}^{2}}\text{ }>\text{ }0,\text{ }\therefore \text{ }f'\left( x \right)\text{ }<\text{ }0\text{ }\Rightarrow \text{ }f(x)\]is decreasing function \[\Rightarrow \] Assertion [A] is true Also Reason [R] is true (Definition of Strictly Decreasing function) Clearly R is correct explanation of A. Hence option [A] is the correct answer.
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